Method of exploiting a hydrocarbon deposit containing organosulfur compounds by means of a thermokinetic model and a compositional

ABSTRACT

Method for determining an amount of hydrogen sulfide produced by a phenomenon of aquathermolysis induced by a thermal process, such as steam injection. 
     The hydrocarbons are described by means of a compositional representation using H 2 S and four fractions: saturated compounds, aromatics, resins and asphaltenes. Then a kinetic model is constructed on the basis of the compositional representation, starting from an elementary model obtained by mass balance for the element sulfur distributed within the fractions. Next, a thermodynamic model is constructed on the basis of the same compositional representation. Finally, the amount of hydrogen sulfide (H 2 S) produced is determined by performing a compositional reservoir simulation by means of a compositional and reactive thermal simulator, with the simulator employing the kinetic model and the thermodynamic model.

The invention relates to the field of oil exploration, and more particularly the field of the exploitation of a deposit of hydrocarbons containing organosulfur compounds, by a thermal process such as a steam injection process.

During the exploitation of reservoirs of heavy crudes by a steam injection process, a phenomenon of aquathermolysis occurs, which generates hydrogen sulfide (H₂S). In fact this type of reservoir often contains high sulfur contents. Thermal processes make it possible, by supplying calories and raising the temperature, to reduce the viscosity of the heavy crudes and thus make them producible.

Aquathermolysis is defined as a set of physicochemical reactions between rock impregnated with crude oil (or with bitumen) and steam, at temperatures between 200° C. and 300° C. A definition is given in the following document: Hyne J. B. et al., 1984, “Aquathermolysis of heavy oils”, 2nd Int. Conf., The Future of Heavy Crude and Tar Sands, McGraw Hill, New York, Chapter 45, p. 404-411.

Hydrogen sulfide is a gas that is both extremely corrosive and highly toxic, or even lethal above a certain concentration. Thus, predicting the concentration of H₂S in the gas produced during recovery assisted by steam injection helps, on the one hand, to reduce the costs of production by adapting the completion materials and the gas treatment devices, by optimizing the operating conditions, and on the other hand to avoid emissions that are dangerous to people and the environment.

One technical problem is prediction of the amount of H₂S generated depending on the nature of the crude, the reservoir conditions and the steam injection conditions. If we wish to predict the risk of production of H₂S based on a reservoir model (used by flow simulators), a kinetic model of hydrogen sulfide generation is indispensable.

A method is known from patent application FR2892817 for constructing a kinetic model for estimating the mass of hydrogen sulfide produced by aquathermolysis of rock containing crude oil, by describing the evolution of the distribution of sulfur in the oil fractions and the insolubles fraction, said document providing an exhaustive review of the state of the art prior to this publication. The method proposed supplies an elementary reaction scheme, for the element sulfur, that is predictive, obtained from the mass balance for the element sulfur distributed within fractions such as resins or asphaltene fractions, but not usable as such in reservoir simulations that use information on constituents of the molecular type, rather than information on atomic elements.

Other thermokinetic models are also known for estimating the mass of hydrogen sulfide produced by aquathermolysis of rock containing crude oil, but these models come up against at least one of the following problems:

-   -   their complexity means they cannot be used in reservoir         simulators for carrying out reservoir simulations;     -   there is no assurance of consistency between the thermodynamic         parameters of the constituents and the reaction scheme (in         particular the stoichiometry of the reactions);     -   the stoichiometric coefficients of the reactions are expressed         in mass fractions rather than in mole fractions;     -   insufficiently precise models (resins not taken into account in         the production of hydrogen sulfide, no description of the         evolution of the distribution of sulfur in the various         fractions, etc.);     -   models without thermodynamic characterization of the         pseudo-constituents;     -   models are not predictive (it is necessary to produce first,         before the models can be established).

The invention relates to a method of exploiting a hydrocarbon deposit containing organosulfur compounds by means of a thermokinetic model and a compositional reservoir simulation. The thermokinetic model constructed in the method according to the invention overcomes the problems of the earlier models.

THE METHOD ACCORDING TO THE INVENTION

In general, the invention relates to a method for determining an amount of hydrogen sulfide produced by a phenomenon of aquathermolysis induced by a thermal process, such as steam injection, applied to an underground deposit of hydrocarbons containing organosulfur compounds. The method comprises the following steps:

-   -   the hydrocarbons are described by means of a compositional         representation using H₂S and four fractions: saturated         compounds, aromatics, resins and asphaltenes;     -   a kinetic model is constructed on the basis of said         compositional representation, starting from an elementary model         obtained by mass balance for the element sulfur distributed         within said fractions;     -   a thermodynamic model is constructed on the basis of said         compositional representation;     -   the amount of hydrogen sulfide (H₂S) produced is determined by         performing a compositional reservoir simulation by means of a         compositional and reactive thermal simulator, said simulator         employing said kinetic model and said thermodynamic model.

According to the invention, the kinetic model can be constructed by considering that the reactants of the reactions of H₂S generation belong to the classes of resins and asphaltenes, and by considering that the products of said reactions belong to the total of H₂S, saturated fractions, aromatic fractions and a pseudo-constituent of the solid type such as coke.

According to the invention, the kinetic model can comprise Nt constituents and Nr reactions, and we then construct a matrix Nr×Nt of stoichiometric coefficients of the various reactions; said stoichiometric coefficients being determined from an elementary reaction scheme obtained by mass balance for the element sulfur.

The kinetic model can be adjusted by simulating aquathermolysis experiments or by simulating the behavior of a field subjected to a thermal process, a field for which production measurements allowing calculation of H₂S production are available. The kinetic model can be adjusted by adjusting time constants for restoring a decrease in resins and asphaltenes as a function of time, or by adjusting the relative stoichiometry between the saturated fractions and the aromatics, or by adjusting the relative stoichiometry between H₂S and a pseudo-constituent of the solid type such as coke.

According to one embodiment, the compositional representation comprises:

-   -   pseudo-constituents for representing fluid phases and phases         that can be made to become fluid, notably by the effect of         temperature;     -   at least one pseudo-constituent of the solid type (COK), such as         coke;     -   at least one constituent representing water.

According to the invention, the fraction of saturated compounds can represent the only fraction of compounds not containing sulfur.

The invention also relates to a method of exploiting an underground deposit of hydrocarbons containing organosulfur compounds, in which:

-   -   i. an amount of hydrogen sulfide (H₂S) produced by a phenomenon         of aquathermolysis induced by a thermal process such as         injection of steam into said deposit is determined by the method         according to the invention;     -   ii. the exploitation conditions of said deposit are determined         as a function of said amount of hydrogen sulfide;     -   iii. said hydrocarbons are produced by applying said         exploitation conditions.

Said amount of hydrogen sulfide can be compared with an amount measured in the past, and parameters of said kinetic model and/or of said thermal model are adjusted.

Production of H₂S by said deposit can be predicted from said adjusted models.

The exploitation conditions can be determined, adapting completion materials and/or gas treatment devices.

The exploitation conditions can be modified by adapting the conditions of steam injection.

Finally, according to the invention said amount of hydrogen sulfide can be compared with a maximum legal content, and the exploitation conditions are determined so as to maintain production of hydrogen sulfide below said maximum legal content.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1—Curve of viscosity of dead oil (10⁻² poise) as a function of temperature (° C.)

FIG. 2.1—Results of simulations of the reactor type (lines) relative to the experimental results (points). On the left: mass fractions of component of the oil produced as a function of time (hours); on the right: mass of H₂S produced relative to the total mass produced of pseudo-constituents SAT, ARO, RES, ASP as a function of time (hours). Results obtained (a) with stoichiometry (1) and the kinetic parameters (1), (b) with stoichiometry (1) and the kinetic parameters (2).

FIG. 2.2—Results of the simulations of the reactor type (lines) relative to the experimental results (points). On the left: mass fractions of component of the oil produced as a function of time (hours); on the right: mass of H₂S produced relative to the total mass produced of pseudo-constituents SAT, ARO, RES, ASP as a function of time (hours). Results obtained (a) with stoichiometry (2) and the kinetic parameters (2), (b) with stoichiometry (3) and the kinetic parameters (3).

FIG. 3—Curves of relative permeabilities (kr) used in the simulations: on the left water-oil kr as a function of water saturation (as a fraction of pore volume), on the right gas-oil kr as a function of gas saturation (as a fraction of pore volume).

FIG. 4.1—Cumulative oil production (millions of m³ at the surface, left axis), ratio of cumulative amounts steam injected/oil produced (equivalent m³ water/m³ oil, right axis), as a function of time (years).

FIG. 4.2—Flow rate of oil produced in surface conditions (m³/day, left axis) and injection well bottom temperature (° C., right axis), as a function of time (years).

FIG. 5—Ratio of liters of H₂S produced per m³ of oil produced as a function of time (years): results (black points and lines) simulated with stoichiometries (2) and (3) and field data (pink points)

FIG. 6—Mole fraction of gas phase after 4 years of production; it is not defined in the zones in gray and in blue, zones where there is no gas phase.

DETAILED DESCRIPTION OF THE METHOD ACCORDING TO THE INVENTION

The words “hydrocarbon” and “hydrocarbons” can be used here, as often in reservoir engineering, in the broad sense: they denote both hydrocarbons in the strict sense (saturated, aromatic) and organosulfur compounds.

Hydrocarbon mixtures are represented, in reservoir simulation, as mixtures of “constituents” and/or “pseudo constituents”. The word “constituent” denotes firstly molecular species such as hydrogen sulfide (H₂S), methane, etc. The word “pseudo-constituent” denotes a mixture of molecular species that can be likened to a single molecular species for the problem under discussion.

Hereinafter, the words “compound”, “component”, “pseudo-compound”, “pseudo-component”, “pseudo-constituent”, “pseudo-constituent”, “constituent” denote species that can be likened to molecular species. The term “constituent” therefore is not necessarily reserved for “pure molecular substances” such as H₂S, CH₄, etc.

The word element, used outside of a mathematical context, is reserved for an elementary atomic species such as sulfur S, carbon C, hydrogen H, etc.

The present invention relates to a method, and the use thereof, for modeling the production of hydrogen sulfide (H₂S) induced by reactions taking place in an underground deposit of hydrocarbons when this deposit is submitted to a thermal recovery process, in particular to a steam injection process, the reactions then being due to a phenomenon of aquathermolysis.

The method according to the invention comprises the following steps:

-   -   i. the amount of hydrogen sulfide (H₂S) produced is determined         by applying the following steps:         -   the hydrocarbons are described by means of a compositional             representation using H₂S and four fractions, saturated             compounds, aromatics, resins and asphaltenes;         -   a thermokinetic model is constructed on the basis of said             compositional representation,         -   the amount of hydrogen sulfide (H₂S) produced is determined             by performing a compositional reservoir simulation by means             of the model;     -   ii. the exploitation conditions of said deposit are determined         as a function of said amount of hydrogen sulfide;     -   iii. said hydrocarbons are produced by applying said         exploitation conditions.

1. Determination of an Amount of Hydrogen Sulfide (H₂S) Produced

The aim of this step is to allow estimation, by compositional reservoir simulation, of the amount of hydrogen sulfide (H₂S) that would be produced if a thermal process is used for exploiting an underground reservoir impregnated with oil or bitumen containing organosulfur compounds.

By anticipating the production of H₂S even before its production, it is possible to optimize the method of exploiting the reservoir.

To estimate this production of H₂S, a compositional reservoir simulation is carried out using two software tools. The first is a thermokinetic model of production of hydrogen sulfide (H₂S) produced during exploitation, and the second tool is a reservoir simulator of the thermal, compositional and reactive simulator type.

The first step therefore consists of constructing the thermokinetic model.

1.1 Construction of a Thermokinetic Model

The crude oil is assumed to consist essentially of Cn+; the fractions making up the Cn—can be present, but it is not indispensable to take them into account in the modeling. For a bitumen, the number of carbons n is typically equal to 14.

A characterization by classes of chemical compounds commonly employed in the industry is the S.A.R.A. characterization, described for example in the following document:

F. Leyssale, 1991, “Investigation of the pyrolysis of alkylpolyaromatics applied to processes for converting heavy petroleum products. Influence of the aromatic nucleus on thermal behavior” (in French), Thesis of the University of Paris VI, IFO Ref. No. 39 363.

It consists of describing the crude oil in four fractions: saturated compounds, aromatics, resins and asphaltenes, and of supplying the mass fraction of each of these fractions in the crude oil. It is assumed that information of the S.A.R.A. type is available for the case of application of the method. It is further assumed that the content by weight of atomic sulfur in each fraction is known (measured or estimated) by elemental analysis, a technique that is well known by a person skilled in the art.

The method according to the invention supplies a thermokinetic model making it possible, using reservoir simulation software (step 1.2), to predict as a function of time, the production of H₂S by reactions of aquathermolysis in an underground reservoir of heavy hydrocarbons submitted to a thermal process of steam injection, or to a process able to vaporize the water naturally present in the reservoir. The reservoir simulation used is based on a compositional representation of the hydrocarbons present in the reservoir, this compositional representation using H₂S, if necessary one or more constituents or pseudo-constituents to represent the Cn− fraction, and, to represent the Cn+ fraction:

-   -   a pseudo-constituent representing the class of compounds not         containing sulfur; this pseudo-constituent is likened to the         class of saturated compounds, and is denoted by SAT,     -   at least one pseudo-constituent representing the class of the         aromatics; this pseudo-constituent is denoted by ARO,     -   one or more pseudo-constituent(s) representing the class of the         resins; these pseudo-components are denoted by RES₁, RES₂, . . .         , RES_(P),     -   one or more pseudo-constituent(s) representing the asphaltene         class; these pseudo-components are denoted by ASP₁, ASP₂, . . .         , ASP_(q).

In addition to these constituents or pseudo-constituents, Nc in number, which make it possible to simulate the fluid phases, or that are to be made fluid, notably by the effect of temperature, the following are represented:

-   -   one or more pseudo-constituents of the solid type such as coke         denoted by COK₁, COK₂, . . . , COK_(s), these solid         pseudo-constituents being Ns in number;     -   at least one constituent representing water, pure water (H₂O)         being useful notably for modeling steam. Liquid water itself can         be salty, as the formation waters generally are, and is         represented otherwise than with H₂O alone.         Each of the sulfur-containing pseudo-constituents {ARO, COK₁,         COK₂, . . . , COK_(s), RES₁, RES₂, . . . , RES_(P), ASP₁, ASP₂,         . . . , ASP_(q)} is likened to a macromolecule of general         formula R_(nR)S_(nS), where S denotes the sulfur atom of mass         M_(S) and R denotes a set of atoms regarded as a single atomic         pseudo-element of mass M_(R), with n_(S), n_(R) denoting the         numbers of atoms S and of pseudo-elements R respectively in the         macromolecule of molecular weight MW. If n_(R) is put equal to         1, the general formula of each macromolecule is RS_(nS). The         relation between MW, n_(S), M_(R) is then written:

MW=n_(S) M _(S) +M _(R)  (1)

The atomic mass of sulfur M_(S) can be taken to be equal to 32.065, the value of the standard atomic mass according to the organization N.I.S.T. (National Institute of Standards and Technology, http://www.nist.gov/pml/data/comp.cfm). M_(R) is introduced here simply to facilitate the presentation.

The content by weight of atomic sulfur w_(S) within the macromolecule, assumed to be known, and which is a defined positive real quantity, is written:

$\begin{matrix} {w_{S} = \frac{n_{S}M_{S}}{M\; W}} & (2) \end{matrix}$

The molecular weight MW is assumed to be known (measured or estimated by a method known per se). The number of sulfur atoms in the macromolecule is deduced simply from:

$\begin{matrix} {n_{S} = \frac{w_{S}M\; W}{M_{S}}} & (3) \end{matrix}$

A Priori Reactive Model According to the Invention

The reactants considered in the reactions used for generating H₂S belong to the classes of resins and asphaltenes, therefore to all of the pseudo-constituents {RES₁, RES₂, . . . , RES_(p), ASP₁, ASP₂, . . . , ASP_(q)}. The reaction products typically belong to the set {H₂S, SAT, ARO, COK₁, COK₂, . . . , COK_(S)}. The reaction system is a set with N_(r)=p+q reactions, which is written:

$\begin{matrix} {{\begin{matrix} \begin{matrix} {{{{{RES}_{j}\overset{K_{{RES}_{j}}{(T)}}{}a_{j\; 1}}H_{2}S} + {a_{j\; 2}{SAT}} + {a_{j\; 3}{ARO}} + {a_{j\; 4}{COK}_{1}} + \ldots}\mspace{14mu},} \\ {{j = 1},\ldots \mspace{14mu},p} \end{matrix} \\ \begin{matrix} {{{{{ASP}_{j}\overset{K_{{ASP}_{j}}{(T)}}{}b_{j\; 1}}H_{2}S} + {b_{j\; 2}{SAT}} + {b_{j\; 3}{ARO}} + {b_{j\; 4}{COK}_{1}} + \ldots}\mspace{14mu},} \\ {{j = 1},\ldots \mspace{14mu},q} \end{matrix} \end{matrix}},\mspace{20mu} {\forall{t \geq 0}}} & (4) \end{matrix}$

with:

T: temperature

t: time

a_(j1), a_(j2), a_(jn): stoichiometric coefficients, defined in such a way that the reactions are balanced in mass

b_(j1), b_(j2), b_(jn) stoichiometric coefficients, defined in such a way that the reactions are balanced in mass

K_(REsj)(T), K_(ASPj)(T): time constants per reaction j: 1≦j≦p or 1≦j≦q

These stoichiometric coefficients can be put in the form of a matrix [α_(rk)] in which the number of rows is equal to the number of reactions Nr and in which the number of columns is equal to Nt=Ns+Nc. A unified formalism is adopted for the Nt constituents and pseudo-constituents, reactants and products, according to which the stoichiometric coefficients of the reactants are negative, those of the products are positive, zero stoichiometric coefficients being attributed to the constituents and/or pseudo-constituents appearing neither as reactant nor as product for a given reaction. Per reaction, there is only a single reactant belonging to the set of pseudo-constituents {RES₁, RES₂, . . . , RES_(p), ASP₁, ASP₂, . . . , ASP_(q)}. The stoichiometric matrix is written on a molar basis. With these conventions, the matrix of the stoichiometric coefficients, normalized per reaction (per row) with the number of moles of reactant, is written with a single value −1 per row or per reaction, this value −1 being located in the column corresponding to the single reacting constituent:

$\begin{matrix} \; & \begin{matrix} {H_{2}S} & {SAT} & {ARO} & {COK}_{1} & {COK}_{2} & \ldots & {COK}_{s} & {RES}_{1} & {RES}_{2} & \ldots & {RES}_{p} & {ASP}_{1} & {ASP}_{2} & \ldots & {ASP}_{q} \end{matrix} \\ \begin{matrix} R_{1} \\ R_{2} \\ \vdots \\ \vdots \\ R_{u} \\ \vdots \\ \vdots \\ R_{r} \end{matrix} & \begin{matrix} \alpha_{11} & \; & \alpha_{12} & \; & \alpha_{13} & \; & \alpha_{14} & \; & \alpha_{15} & \; & \alpha_{1\mspace{14mu} \ldots} & \alpha_{1\; s} & \; & {- 1} & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & 0 \\ \alpha_{21} & \; & \alpha_{22} & \; & \alpha_{23} & \; & \alpha_{24} & \; & \alpha_{25} & \; & \alpha_{2\mspace{14mu} \ldots} & \alpha_{2\; s} & \; & 0 & \; & {- 1} & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & 0 \\ \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots \\ \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots \\ \alpha_{u\; 1} & \; & \alpha_{u\; 2} & \; & \alpha_{u\; 3} & \; & \alpha_{u\; 4} & \; & \alpha_{u\; 5} & \; & \alpha_{u\mspace{14mu} \ldots} & \alpha_{u\; s} & \; & 0 & \; & 0 & \; & 0 & \; & {- 1} & \; & 0 & \; & 0 & \; & 0 & \; & 0 \\ \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots \\ \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots & \; & \vdots \\ \alpha_{r\; 1} & \; & \alpha_{r\; 2} & \; & \alpha_{r\; 3} & \; & \alpha_{r\; 4} & \; & \alpha_{r\; 5} & \; & \alpha_{r\mspace{14mu} \ldots} & \alpha_{r\; s} & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & 0 & \; & {- 1} \end{matrix} \end{matrix}$

For every value of the row index r there is therefore a corresponding single value k, designated k(r), for which:

α_(rk)=−1  (5)

This value of k is denoted k(r).

The stoichiometric coefficients α_(rk) must satisfy Nr equations of conservation of mass which are written:

${{\sum\limits_{k = 1}^{N\; t}{\alpha_{rk}M\; W_{k}}} = 0.},{1 \leq r \leq {N\; r}},$

the α_(rk) being expressed in mole fractions (6)

with:

r: row index or reaction number

k: column index that refers to a given constituent, pseudo or not, in the list of constituents and pseudo-constituents.

MW_(k) molecular weight of constituent k.

According to the invention, a first estimate of the stoichiometric coefficients α_(rk) is obtained:

-   -   by a zero value for the column corresponding to the         pseudo-constituent SAT; this constituent is classified here as         number 2: α_(r2)=0.     -   from the equation: α_(rk)=e_(rk)t_(rk)(7), for the other         columns, with:

e_(rk): the stoichiometric coefficients of an elementary kinetic model giving the distribution of sulfur in the various constituents and pseudo-constituents, presented below in the next paragraph,

t_(rk): the elements of a transformation matrix, defined by the equation:

$\begin{matrix} {{t_{rk} = \frac{n_{{Sk}{(r)}}}{n_{Sk}}},} & (8) \end{matrix}$

where n_(Sk), n_(Sk(r)) denote respectively the number of sulfur atoms in the constituent k and in the constituent k(r), these numbers of atoms being obtained from equation (3).

On rearranging equation (6), we then obtain the stoichiometric coefficients of the constituent SAT:

$\begin{matrix} {\alpha_{r\; {SAT}} = {{- \frac{1}{M\; W_{SAT}}}{\sum\limits_{k \neq {SAT}}{\alpha_{rk}M\; W_{k}}}}} & (9) \end{matrix}$

The stoichiometric coefficients e_(rk) are typically taken from the elementary kinetic model defined by Lamoureux-Var and Lorant (2007) and described in patent application FR2892817, which is constructed on the distribution of all the sulfur in the different fractions of the Cn+ cut (n typically equal to 14) with the following considerations:

-   -   it is considered that the saturated compounds fraction does not         contain sulfur;     -   it is considered that the sulfur contained in the resins         fraction gives rise to hydrogen sulfide and is incorporated         partly in the insolubles and aromatics fractions;     -   it is considered that the sulfur contained in the asphaltenes         fraction gives rise to hydrogen sulfide and is incorporated         partly in the insolubles and aromatics fractions;     -   it is further assumed that the sulfur in the asphaltenes and the         sulfur in the resins do not interact;     -   moreover, it is considered that several reactions coexist in         parallel within each fraction, these reactions being         characterized by different time constants.

The reaction system considered in this elementary kinetic model constructed on the distribution of sulfur is written as:

$\begin{matrix} {{\begin{matrix} \begin{matrix} {{{{S^{RESj}\overset{K_{S^{RESj}}{(T)}}{}u_{j\; 1}}S^{H\; 2\; S}} + {0{SAT}} + {u_{j\; 3}S^{ARO}} + {u_{j\; 4}S^{{COK}_{1}}} + \ldots}\mspace{14mu},} \\ {{j = 1},\ldots \mspace{14mu},p} \end{matrix} \\ \begin{matrix} {{{{S^{ASPj}\overset{K_{S^{ASPj}}{(T)}}{}v_{j\; 1}}S^{H\; 2\; S}} + {0S^{SAT}} + {v_{j\; 3}S^{ARO}} + {v_{j\; 4}S^{{COK}_{1}}} + \ldots}\mspace{14mu},} \\ {{j = 1},\ldots \mspace{14mu},q} \end{matrix} \end{matrix}},\mspace{20mu} {\forall{t \geq 0}}} & (10) \end{matrix}$

where S^(H2S), S^(RESj), S^(ASPj), S^(ARO), S^(COK) ¹ , S^(ASPj), . . . , denote respectively the sulfur contained in H₂S, the resin fraction RES_(j), the asphaltene fraction ASP_(j), the aromatic fraction ARO, the fraction COK₁, . . . , the different species of sulfur considered therefore being differentiated by the molecular nature of their containment.

with:

T temperature

t time

u_(j1), u_(j2), u_(jn): stoichiometric coefficients, defined in such a way that the reactions are balanced in mass stoichiometric coefficients, defined

v_(j1), v_(j2), v_(jn): in such a way that the reactions are balanced in mass

K_(s)REs_(j)(T), K_(s)AsP_(j)(T): time constants per reaction j: 1≦j≦p or 1≦j≦q.

The reaction kinetic constants are typically calculated from:

$\begin{matrix} {{K_{r}(T)} = {A_{r}{{Exp}\left( \frac{- E_{r}}{R\; T} \right)}}} & (11) \end{matrix}$

with:

R the ideal gas constant (R=8.314 J.K⁻¹.mol⁻¹)

A_(R): pre-exponential factor, also denoted by the expression “frequency factor”, of reaction r

E_(r): activation energy of reaction r.

The stoichiometric coefficients e_(rk) introduced above in matrix notation are easily deduced by identification with the reaction system (10) by assigning a stoichiometric coefficient of −1 to the only reacting sulfur species (column index k equal to k(r)) of each reaction r.

The reactive model according to the invention, written on the basis of molecular species, being modeled on the elementary kinetic model defined by Lamoureux-Var and Lorant (2007), naturally inherits kinetic parameters from the elementary kinetic model:

K _(RESj)(T)≡K _(S) _(RESj) (T) 1≦j≦p

K _(ASPj)(T)≡K _(S) _(ASPj) (T) 1≦j≦q  (12)

In the method according to the invention, it is noted that:

-   -   the molecular weight of the various pseudo-constituents         considered {SAT, ARO, RES_(T), RES₂, . . . , RES_(p), ASP₁,         ASP₂, . . . , ASP_(q)} for representing the Cn+ fraction and         {COK₁, COK₂, COK_(s)} is an intrinsic data element, and as         assumed by definition, the molecular weight of a constituent is         a constant parameter, invariant over time;     -   in the set {SAT, ARO, RES₁, RES₂, . . . , RES_(p), ASP₁, ASP₂, .         . . ASP_(q), COK₁, COK₂, . . . , COK_(s)} only the         pseudo-constituent SAT representing the saturated compounds does         not contain sulfur. It follows from this that all the other         constituents including the COK_(k) contain sulfur.

A Priori Thermodynamic Model According to the Invention

In reservoir simulation, it is necessary to have a thermodynamic model for estimating the properties or the behavior of the liquid and/or vapour phases of mixtures of multiple components, such as are encountered in situ in reservoirs of oil, bitumen or gas, or at the surface during exploitation of these same deposits, and offering the possibility of predicting, as a function of time, the detailed composition of fluids produced in the course of production.

In the reactive context of the invention, it is necessary to have a compositional thermodynamic model where the compositions of the non-aqueous and non-solid phases are detailed using the same compositional base as the reactive model, namely for the Cn+ cut, on the basis of the constituents of the set {SAT, ARO, RES₁, RES₂, . . . , RES_(p), ASP₁, ASP₂, . . . , ASP_(q)}.

The solids {COK₁, COK₂, . . . , COK_(s)} are only characterized by their molecular weight alone, the very same that was used in equations (2) and (3), and are not considered in the calculation of the properties of the oil, gas and water phases.

The molecular weight of each of the constituents {SAT, ARO, RES₁, RES₂, . . . , RES_(p), ASP₁, ASP₂, . . . , ASP_(q)} is identical to what was used for constructing the reaction model.

The other thermodynamic parameters of each of the constituents {SAT, ARO, RES₁, RES₂, . . . , RES_(p), ASP₁, ASP₂, . . . , ASP_(q)} are correlated, by a known method per se, with their molecular weight.

If we choose to use thermodynamics by correlation, the parameters of constituents in the correlations can be adjusted on the basis of calculations carried out with an equation of state where the parameters per constituent are typically obtained from databases when “pure substances” are involved, such as H₂S (or for example such as normal pentane if we choose to introduce this constituent in the description of Cn−), or, when pseudo-constituents are involved, on the basis of correlations based at least partly on the molecular weight.

Estimation of Molecular Weights

The a priori estimation of the molecular weights of the pseudo-constituents can be based on:

-   -   measurements of molecular weights of SARA fractions carried out         before or after a certain length of time/certain lengths of time         in conditions of aquathermolysis;     -   and/or elemental analyses of the various SARA fractions carried         out before or after a certain length of time/certain lengths of         time in conditions of aquathermolysis;

and/or a database of molecular weights of SARA fractions constituted from elements found in the literature, or from private elements.

-   -   The a priori estimates of the molecular weights can be refined         by a process of optimization under constraint:     -   for example to reproduce measurements of molecular weights on         the crude or the bitumen taken together, measurements carried         out before or after a certain length of time/certain lengths of         time in conditions of aquathermolysis;     -   for example taking them as parameters of adjustment of         simulations, at the scale of the aquathermolysis reactor,         intended to reproduce the experimentally measured evolution of         the mass fractions of the H₂S, saturated compounds, aromatics,         resins and asphaltenes;     -   for example taking them as parameters of adjustment of         simulations, at the scale of the reservoir, intended to         reproduce the production of H₂S as measured on a field exploited         by a thermal process.

To preserve consistency between the reaction model and the thermodynamic model, the thermodynamic parameters of the pseudo-constituents should be made to evolve consistently with the evolution of their molecular weight.

Thus, at the end of this step, we have

-   -   constructed a thermodynamic representation with number Nc of         components and/or pseudo-components usable for estimating the         properties or the behavior of the liquid and/or vapour phases of         mixtures of multiple components, such as are encountered in situ         in the reservoirs of oil or gas or at the surface during         exploitation of these same deposits,     -   constructed the reaction scheme associated with the Nc         components, with Nr reactions, in particular the matrix Nr×Nc of         the stoichiometric coefficients of the various reactions, this         reaction scheme being constructed on the basis of an elementary         reaction scheme obtained by mass balance for the element sulfur         distributed within fractions such as resins or asphaltene         fractions.

1.2 Carrying Out the Reservoir Simulation

In oil and/or gas field engineering, a reservoir simulator (also called formation simulator) is a software tool for simulating the processes for exploitation of underground reservoirs of hydrocarbons. Modeling of the flows in an oil reservoir or in underground storage is based essentially on application to the reservoir previously interconnected (or to a portion of the latter) of Darcy's well known law describing the flow of fluids in porous media, of laws of mass balance in each volume unit, of thermodynamic relations governing the evolution of the phase properties of the fluids such as viscosity, density, on the initial conditions, on boundary conditions of closure of the structure, and on conditions at the producing wells and/or injectors. In the context of the invention, the software tool must permit simulation of steam injection in a heavy oil deposit taking into account the thermal effects in a chemically reactive context, the hydrocarbons (in the broad sense) being represented as multi-constituent mixtures. The formation simulator is then called thermal, compositional and reactive. An example of such a tool is the PumaFlow software (2012).

In compositional reservoir simulation with presence of steam, the phase equilibria between the “aqueous liquid” (called “water”), “hydrocarbon liquid” (called oil), and gas phases are calculated typically using the following hypotheses:

-   -   the gas phase contains steam, and at least the lightest of the         constituents of the “hydrocarbon” type, here H₂S;     -   the oil phase contains all the constituents called         “hydrocarbons”, but does not contain water;     -   the “water” phase is essentially more or less salty water, and         an option of dissolution in the aqueous phase of constituents of         the “hydrocarbon” type can be activated for example for H₂S,         which, like carbon dioxide (CO₂), can dissolve considerably in         an aqueous phase.

Calculations of Equilibrium Between Phases

The equilibria between phases are calculated on the basis of equilibrium constants per constituent calculated during simulation (or pre-calculated before the simulation) from fugacities per constituent per phase, themselves obtained from an equation of state, typically a cubic equation of state:

-   -   for the sharing of the constituents between oil and gas phases,         one of the most commonly used equations is the so-called         Peng-Robinson equation, described in the following two         documents:

Peng, D. Y., and Robinson, D. B. 1976. A New Two-Constant Equation of State. Industrial and Engineering Chemistry Fundamentals, 15, 59-64.

Peng, D. Y., and Robinson, D. B. 1978. The Characterization of the Heptanes and Heavier Fractions for the GPA Peng-Robinson Programs. Gas Processors Association, Research Report 28, Tulsa, 1978

-   -   for the sharing of the constituents between gas and water         phases, the most commonly used equation is that of Søreide and         Whitson described in the following document:

Søreide, I. and Whitson, C. H. 1992. Peng-Robinson Predictions for Hydrocarbons CO₂, N₂, and H₂S with Pure Water and NaCl Brine. Fluid Phase Equilibria, 77, 217-240.

Commercial reservoir simulation software packages also offer the possibility of calculating the equilibria between phases from tabulated equilibrium constants, as a function of pressure and temperature and possibly as a function of a compositional index, introduced by the engineer as input data of the simulation.

Another possibility offered for the gas/oil equilibria is that the equilibrium constants are calculated from analytical correlations, the engineer then having to input the parameters of each constituent in the correlations. These two possibilities, tabulated equilibrium constants or from analytical correlation, are those that are offered primarily by commercial software in the reaction and thermal context, and a description of these options can be found in the following publication:

Coats, K. H.1980. In-Situ Combustion Model. SPE Journal, December, 533-554

Provided the inputs for calculating the equilibria are tabulated equilibrium constants per constituent or by correlation, a methodology employed by a person skilled in the art is to generate the tables or the parameters of the constituents from a reference equation of state. The tables must be generated for pressures and temperatures that may be encountered in the course of numerical reservoir simulation.

The parameters of the constituents in the reference equation of state are typically the critical parameters (temperature, pressure, volume or compressibility factor), the acentric factor, parameters of binary interactions between constituents.

The thermodynamic parameters of pure substances such as H₂S are known and are listed by various organizations such as N.I.S.T. (National Institute of Standards and Technology, http://www.nist.gov). In contrast, the parameters of pseudo-constituents, critical parameters, acentric factor, and parameters of binary interactions must be estimated. Numerous correlations are available, including correlations based on the molecular weight of the pseudo-constituent, its density and its boiling point, and these last two properties can themselves be estimated by correlations based on the molecular weight of the pseudo-constituent. As a guide for selecting the correlations to use, it is possible to make use of certain information relating to the nature of the pseudo-constituent (such as an elemental analysis that gives the mass distribution of different atomic elements), and/or to its structure, taking inspiration for example from Boduszynski's work:

Boduszynski, M. M. 1987. Composition of Heavy Petroleums. 1. Molecular Weight, Hydrogen Deficiency, and Heteroatom Concentration as a Function of Atmospheric Equivalent Boiling Point up to 1400° F. (760° C.). Energy & Fuels, 1, 2-11

Finally, it should be added that the measured value of the molecular weight of heavy compounds is known to depend on the experimental technique used, for example as reported by:

Merdrignac, I. and Espinat D. 2007. Physicochemical Characterization of Petroleum Fractions: the State of the Art. Oil & Gas Science and Technology—Rev. IFP, 62, 1, 7-32

Whatever the level of sophistication of the method used for determining them, the molecular weights of the heavy pseudo-constituents therefore are still estimates, which can be used as first estimates in a process of optimization of parameters, or are not to be modified if they are considered to be sufficiently representative, or if it is found a posteriori that the values adopted a priori were a judicious choice.

Calculations of Phase Properties

The phase properties useful for the calculations carried out in numerical compositional reservoir simulation are, per phase: viscosity, enthalpy, molecular weight, molar density (inverse of molar volume), the product of these last two properties being equal to the density, estimation of which is indispensable for the calculations of the gravity effects, the latter in fact being linked to the density differences between phases. The molecular weights of the phases can be calculated directly from the results of the equilibrium calculations that supply the compositions of each phase.

Various possibilities are offered for calculating the molar volumes of the oil and gas phases:

-   -   from an equation of state, typically cubic, generally identical         to that used for the equilibrium calculations, using the same         parameters per constituent as those that are used for         calculating the equilibria;     -   from correlations differentiated according to the nature of the         oil or gas phase, these correlations using specific parameters         defined per constituent.

For calculating the viscosities, it is possible to use a single correlation for the calculations of viscosity of the oil and gas phases or, more often for the simulation of heavy oil reservoirs, one correlation for the viscosity of the oil and a different correlation for the viscosity of the gas. These correlations use specific parameters defined per constituent.

The enthalpies of the phases are usually calculated from specific heats defined per constituent and per phase, and the specific heat per constituent in the gas phase can alternatively be calculated from a specific heat per constituent in the oil phase and from a latent heat per constituent.

Further details can be found in the work of Coats cited above, in that of Crookston, and in the reference manuals of commercial reservoir simulation software such as PumaFlow.

Crookston, R. B., Culham, W. E., Chen, W. H.1979. A Numerical Simulation Model Recovery Processes for Thermal Recovery Processes. SPE 6724, SPE J., Feb., 37-58.

The method according to the invention therefore makes it possible to model hydrocarbon fluids in a mixture of constituents, each of these constituents being characterized by thermodynamic parameters for modeling the physical properties of the fluid, this thermodynamic modeling moreover being consistent with a multi-reaction kinetic model, where one of the products of the reactions modeled is hydrogen sulfide (H₂S).

At the end of this step, a so-called “reservoir” simulation gives the amounts of H₂S that can be generated during the exploitation of oil deposits by steam injection.

2. Determination of the Exploitation Conditions as a Function of the Amount of Hydrogen Sulfide

These amounts of hydrogen sulfide can be compared to an amount measured in the past (production history). It is then possible to adjust the parameters of the kinetic model and/or of the thermal model, in such a way that the estimates are more accurate for the deposit under investigation. With these adjusted models it is possible to predict the production of H₂S from the deposit, for given exploitation conditions.

It is also possible to determine the exploitation conditions on adapting the completion materials and/or the gas treatment devices, so as to limit the damage caused by acid attack.

It is also possible to modify the conditions of steam injection in an attempt to reduce the amounts of H₂S produced.

It is also possible to compare the amount of hydrogen sulfide against a maximum legal content (from 10 to 50 ppm by volume, according to the following organization: Agency for Toxic Substances & Disease Registry of the United States), and then determine the exploitation conditions so as to keep the production of hydrogen sulfide below this maximum legal content.

3. Production of Hydrocarbons

By applying the exploitation conditions determined in step 2, for example the amount, flow rate, and temperature of the steam injected, or the type of material, the hydrocarbons are produced observing the legal requirements and minimizing the impact on the equipment.

NONLIMITING EMBODIMENT EXAMPLE

The example described below was carried out using the PumaFlow simulator as a commercial tool for reservoir simulation, but other commercial reservoir simulation software could have been used instead of this simulator. The three fluid phases represented are an aqueous phase, a so-called oil phase, and a gas phase. This software is used here for modeling steam injection in a heavy oil reservoir taking into account thermal and compositional effects in a chemically reactive context. Options employed conventionally in compositional and thermal reservoir simulation are selected for calculating the phase equilibria and the phase properties:

-   -   the use of tables of equilibrium constants per constituent for         calculating the gas/oil equilibria, all the organic         pseudo-constituents and the H₂S being assumed to be shared         between the oil phase and the gas phase;     -   the use of tables of gas-water equilibrium constants for the         H₂S, the only constituent assumed to dissolve in the aqueous         phase;     -   the use of correlations for calculating the properties of the         oil and gas phases (density, viscosity, enthalpy), the         parameters per constituent used in these correlations partly         being tabulated as a function of temperature (and of pressure,         for the parameters involved in calculating the densities).

Thermokinetic Modeling

Aquathermolysis experiments were conducted on samples of bitumen originating from Fisher Field Athabasca, some of the results having been published in Lamoureux-Var et al. (2010).

The results of these aquathermolysis experiments were interpreted in terms of distribution of sulfur in the various fractions, and are reflected in the following stoichiometric matrix:

TABLE 1 STOICHIOMETRIC MATRIX [e_(rk)] RESULTING FROM THE AQUATHERMOLYSIS EXPERIMENTS Reaction Reactant S(H₂S) S(SAT) S(ARO) S(RES1) S(RES2) S(ASP1) S(ASP2) S(COK) R1 S(RES1) 0 0.60 0.38 −1 0 0 0 0.40 R2 S(RES2) 1.00 0 0.00 0 −1 0 0 0.00 R3 S(ASP1) 0.00 0 0.00 0 0 −1 0 1.00 R4 S(ASP2) 0.07 0 0 0 −1 0.33 and of the kinetic constants per reaction according to equation (11), which are calculated using, per reaction, a frequency factor and an activation energy. The frequency factors are given in the following table.

TABLE 2 FREQUENCY FACTORS, DAY-1 Reaction (1) R1 8.64E+18 R2 8.64E+18 R3 8.64E+18 R4 8.64E+18

Table (1) shows that interpretation of the experimental results required the introduction of two species of resins and two species of asphaltenes.

The aquathermolysis experiments are carried out by putting known amounts of crude oil, of rock, and of water in a gold tube placed after evacuation of the air under nitrogen confinement. The tube, once sealed, is put in a chamber maintained at constant pressure, and in turn the chamber is put in a furnace maintained at constant temperature, for a given length of time. The experiments are conducted at different temperatures and for different durations. On leaving the furnace, the gold tubes are cooled, pierced in a controlled environment, then the contents of the gold tubes are analyzed and quantified by mass, separating: the gases, which are recovered by evacuation at 10-5 bar, and analyzed by gas chromatography, C14+ which undergoes a SARA analysis and the insoluble fraction, elemental analyses being carried out on the SARA fractions, and on the insoluble fraction.

The thermokinetic modeling for the reservoir simulations is based on the following hypotheses and simplifications:

-   -   the oil considered is, in its initial state, a C14+ cut;     -   a description of the SARA type is adopted with 4         pseudo-constituents (called SAT, ARO, RES, ASP), the         pseudo-constituents RES and ASP each being split into two         pseudo-constituents, respectively RES1, RES2 and ASP1, ASP2,         which makes it possible to represent the reactions, as         introduced by an elementary kinetic model based on the sulfur         distribution;     -   a single solid reaction product constituent is considered,         called COK, to represent the solid residue receiving the sulfur         coming from the organosulfur pseudo-constituents.

The results of the elemental analyses are taken into account, by a known method per se, for fixing the a priori values of the molecular weights of the pseudo-constituents.

First, a Peng-Robinson equation of state (EOS) is used for modeling the density of the oil and gas phases; a first estimate of the parameters of the pseudo-constituents in the EOS is obtained using correlations based on the molecular weight:

-   -   for the critical parameters:     -   Souahi, F. and Kaabeche, H.2008. Developing Correlations for         Prediction of Petroleum Fraction Properties using Genetic         Algorithms, OGST, 63, No. 2, March-April, 229-237;     -   for the acentric factors, a private correlation inspired by that         proposed by Souahi et al. (2008);     -   for the parameters of binary interactions of the         pseudo-constituents with H₂S:     -   Stamataki, S, and Magoulas, K. 2000. Prediction of Phase         Equilibria and Volumetric Behavior of Fluids with High         Concentration of Hydrogen Sulfide. Oil & Gas Science and         Technology—Rev. IFP, 55, 5, 511-522;     -   for the volume corrections:

Loria, H, Pereira-Almao, P. and Satyro, M. 2009. Prediction of Density and Viscosity of Bitumen Using the Peng-Robinson Equation of State. Ind. Eng. Chem. Res., 48, 10129-10135;

These parameters were adjusted for setting a specific gravity of the crude of 10 degrees API.

For the specific heats of the pseudo-constituents, we used the correlation of Dadgostar and Shaw (2012) based on the number of atoms per mass unit, this information being obtained from the estimate of the molecular weight and from measurements of elemental analyses:

-   -   Dadgostar, N., Shaw, J. M. 2012. A Predictive Correlation for         the Constant-Pressure Specific Heat Capacity of Pure and         Ill-Defined Liquid Hydrocarbons. Fluid Phase Equilibria, 313,         211-226;

The specific gravities and the boiling points per constituent required for certain correlations were obtained by correlation with the molecular weight.

Table 3 presents the parameters of the pseudo-constituents thus obtained:

TABLE 3 EOS PARAMETERS OF THE PSEUDO-CONSTITUENTS Name MW, g Tc, ° C. Pc, bar ω Cv, cm³ δH₂S SAT 195.11 435.95 19.26 0.5875 17.4 0.01489 ARO 930.38 759.47 8.51 1.4115 −131.5 −0.10854 RES1 1324.40 808.81 7.71 1.5509 −344.9 −0.12942 RES2 1318.43 808.26 7.72 1.5494 −341.3 −0.12919 ASP1 2702.30 868.77 7.02 1.7106 −1313.4 −0.15335 ASP2 2691.02 868.56 7.02 1.7101 −1305.0 −0.15327 COK 15.06

Calculations of thermodynamic equilibria were carried out with specialized software, called “PVT Package” by a person skilled in the art, at various pressures and temperatures, and varying the compositions of the mixtures. The density results from these calculations were taken as reference for obtaining the parameters of the constituents in the correlations for calculating the densities, and the compositions of the phases were used for generating the tables of gas/oil equilibrium constants as a function of the pressure and temperature.

The equilibrium constants for the gas-water system were generated using the Søreide-Whitson equation of state (1992).

As the oil phase is not modeled as a dead oil, the modeling of oil viscosity must take account of the possible presence of H₂S (in small amounts) in the oily phase. A table of the viscosities per constituent relative to temperature was generated somewhat empirically, but in order to obtain a viscosity behavior of the dead oil probable for the Foster Creek sector. The viscosity curve of the dead oil as simulated with these tables is illustrated in FIG. 1 as a function of temperature.

The matrix of the stoichiometric coefficients based on the pseudo-constituents, obtained directly from the stoichiometric matrix based on the sulfur distribution given in Table 1 using equations (7), (8) and (9), is given in Table 4.

TABLE 4 STOICHIOMETRIC MATRIX [α_(rk)] (1) FOR THE RESERVOIR SIMULATIONS Reaction Reactant H₂S SAT ARO RES1 RES2 ASP1 ASP2 COK R1 RES1 0.4950000 2.8579821 0.5979021 −1 0 0 0 12.8571429 R2 RES2 2.1000000 6.3905081 0.0000000 0 −1 0 0 0.0000000 R3 ASP1 0.0000000 7.8735564 0.0000000 0 0 −1 0 77.4285714 R4 ASP2 0.3514000 1.8603513 2.1062937 0 0 0 −1 23.6657143

In the various simulations of the experimental reactor, the results of which are presented below, certain adjustments were made to the stoichiometric coefficients. That is why this first version of the stoichiometric matrix is identified with the label (1).

Simulations of the Aquathermolysis Experiments Using Reservoir Simulation Software

The aquathermolysis experiments were simulated with a reservoir simulator for validating the thermokinetic model.

In the simulation model, a single cell is used for representing the experimental “reactor” (the gold tube). This cell is surrounded by cells representing the furnace. Only heat flows are permitted between the “reactor” cell and the surrounding cells. Moreover, the “reactor” cell is not perforated by any well: it is therefore “sealed” like the experimental reactor. The “reactor” cell is initialized with the same proportions of sand, oil, water, and nitrogen (constituent added to the list of the aforementioned constituents) as in the experiments, and the initial pressure is fixed at 100 bar, the pressure used in the experiments. The reactor temperature is fixed at 320° C., which is the highest temperature used for the aquathermolysis experiments.

The results of different simulations are compared against the experimental results in FIGS. 2.1 and 2.2. These figures show, on the left, the evolution as a function of time of the mass fractions of the pseudo-constituents SAT, ARO and of the mass fractions RES and ASP corresponding respectively to the sum of the mass fractions RES1 and RES2 and to the sum of the mass fractions ASP1 and ASP2. These figures show, on the right, as a function of time, the mass of H₂S relative to the sum of the masses of the pseudo-constituents SAT, ARO, RES1, RES2, ASP1, ASP2. The points are the experimental results, and the lines are the simulated results.

The results presented in FIG. 2.1( a) were obtained with stoichiometry (1), the activation energies and the frequency factors (Table 2) resulting directly from interpretation of the experiments. It can be seen that the simulated reaction rates are too high relative to those observed experimentally. The results presented in FIG. 2.1( b) were obtained still with stoichiometry (1), keeping the same activation energies but with frequency factors reduced by about a factor of 2 (data in column 2 of Table 5), which is still a very modest adjustment.

TABLE 5 FREQUENCY FACTORS, DAY-1 Reaction (2) (3) R1 4.50E+18 4.50E+18 R2 4.50E+18 4.50E+18 R3 4.50E+18 3.50E+18 R4 4.50E+18 4.50E+18

With this modification of the frequency factors, we obtain (cf. FIG. 2.1( b)) good adjustment of the time-dependent decrease of the mass fractions of resins (RES1+RES2) and of asphaltene (ASP1+ASP2), but the simulated production of saturated compounds (SAT) increases too much, at the expense of the production of aromatics (ARO), relative to the experimental results, and the production of H₂S is not reproduced.

Since the stoichiometry of the pseudo-constituent SAT, not containing sulfur, is not obtained directly from the experimental results, but by applying a mass balance equation, it absorbs all the experimental uncertainties. Moreover, according to the Lamoureux-Var model (2007), the sulfur contained in the aromatics does not participate in the generation of H₂S (non-labile sulfur). An adjustment of the SAT/ARO stoichiometry is therefore considered to be indicated, without altering the other coefficients. For this purpose, in a reaction r, starting from the stoichiometric coefficients α_(rSAT) and α_(rARO), a new value is fixed for the stoichiometric coefficient α′_(rSAT) of the pseudo-constituent SAT, and the coefficient α′_(rARO) is recalculated in such a way that the mass balance of the reaction is still respected, i.e. so that:

α′_(rSAT)MW_(SAT)+α′_(rARO)MW_(ARO)=α_(rSAT)MW_(SAT)+α_(rARO)MW_(ARO)  (13)

whence:

$\begin{matrix} {\alpha_{r\; {ARO}}^{\prime} = {{\left( {\alpha_{rSAT} - \alpha_{rSAT}^{\prime}} \right)\frac{M\; W_{SAT}}{M\; W_{ARO}}} + \alpha_{rARO}}} & (14) \end{matrix}$

Table (6) repeats stoichiometric matrix (1) and gives the details of the stoichiometric matrix (2) used for adjusting the production of the saturated compounds and aromatics, as illustrated in FIG. 2.2 (a). Bold characters are used for highlighting the differences between matrices (1) and (2). It can be seen in FIG. 2.2 (a) that there is good agreement between simulated results and experimental results regarding evolution of the SARA fractions, but the simulated production of H₂S is still much lower than the experimental production of H₂S.

The stoichiometric matrix (3) given in Table (6) makes it possible to reproduce the production of H₂S obtained experimentally. This is illustrated in FIG. 2.2 (b). The bold characters highlight the modified coefficients. It can be seen that the stoichiometry of COK has been reduced and the stoichiometry of H₂S has been increased, in such a way that the mass balance of the reaction is still respected, i.e. so that:

α′_(rH2S)MW_(H2S)+a′_(rCOK)MW_(COK)=α_(rH2S)MW_(H2S)+α_(rCOK)MW_(COK)  (15)

whence:

$\begin{matrix} {\alpha_{{rH}\; 2S}^{\prime} = {{\left( {\alpha_{rCOK} - \alpha_{rCOK}^{\prime}} \right)\frac{M\; W_{COK}}{M\; W_{H\; 2S}}} + \alpha_{{rH}\; 2S}}} & (16) \end{matrix}$

TABLE 6 STOICHIOMETRIC MATRIXES [α_(rk)] FOR THE RESERVOIR SIMULATIONS Reaction Reactant H₂S SAT ARO RES1 RES2 ASP1 ASP2 COK Stoichiometric matrix (1) R1 RES1 0.4950000 2.8579821 0.5979021 −1 0 0 0 12.8571429 R2 RES2 2.1000000 6.3905081 0.0000000 0 −1 0 0 0.0000000 R3 ASP1 0.0000000 7.8735564 0.0000000 0 0 −1 0 77.4285714 R4 ASP2 0.3514000 1.8603513 2.1062937 0 0 0 −1 23.6657143 Stoichiometric matrix (2) R1 RES1 0.4950000 2.8579821 0.5979021 −1 0 0 0 12.8571429 R2 RES2 2.1000000 6.3905081 0.0000000 0 −1 0 0 0.0000000 R3 ASP1 0.0000000 0.7000000 1.5043795 0 0 −1 0 77.4285714 R4 ASP2 0.3514000 1.8603513 2.1062937 0 0 0 −1 23.6657143 Stoichiometric matrix (3) R1 RES1 0.4950000 2.8579821 0.5979021 −1 0 0 0 12.8571429 R2 RES2 2.1000000 6.3905081 0.0000000 0 −1 0 0 0.0000000 R3 ASP1 5.9341046 0.7000000 1.5043795 0 0 −1 0 64.0000000 R4 ASP2 0.3514000 1.8603513 2.1062937 0 0 0 −1 23.6657143

Modifying the distribution of sulfur between the solid and the H₂S therefore allows calibration of the experimental results. It should be noted, moreover, that H₂S is recognized to have high capacity for adsorption on solids related to coke.

It has been shown that H₂S has the capacity to be adsorbed on coke with a large specific surface. It therefore follows that the H₂S generated by aquathermolysis in given conditions of pressure and temperature could be adsorbed on the organic solid residue generated by the reactions (potentially similar to coke), or also on the mineral solids.

The experimental protocol used for distributing the sulfur between the various fractions after the aquathermolysis experiments comprises depressurization, followed by evacuation, and cooling of the aquathermolysis reactors. It therefore follows that, since the H₂S was adsorbed on solid species in the aquathermolysis reactor, the experimental protocol can induce at least partial desorption of the adsorbed H₂S. This desorption would not have occurred if the gas and oil samples were taken while keeping the reactor under pressure and temperature.

It therefore follows that the amount of H₂S measured experimentally represents a maximum potential production of H₂S, and a phenomenon of adsorption on solids can maintain a proportion of the H₂S generated by aquathermolysis in the reactor maintained at pressure and temperature.

According to one of the features of the invention, such a phenomenon of adsorption can be taken into account by a relative change of the H₂S/COK stoichiometry in the reaction system considered for modeling the production of H₂S by aquathermolysis.

Simulation of the Production of H₂S During Exploitation of a Heavy Oil Reservoir Submitted to a SAGD Process

The reservoir model that was used in the simulations reported here is a cutting plane of the reservoir in a grid in two directions X and Z (Z: depth). The reservoir is homogeneous; the properties are shown in Table 7. The initial composition of the reservoir crude is found directly from the experimental measurements carried out on the samples of the deposit. The other properties are general properties that are probable for an Athabasca bituminous sand exploited by a SAGD process. The curves of relative permeabilities used in the simulations are presented in FIG. 3. The reservoir is exploited by means of two horizontal wells, a producer and an injector, drilled perpendicularly to the cutting plane. As an aquifer zone is present at the bottom of the reservoir, the producer is located at about 8 m above the water-oil contact, and the injector about 5.5 m above the producer. After a preheating time, saturated steam (of 0.95 grade) is injected. After about 250 days of steam injection, the injection pressure is kept approximately constant and equal to 32.5 bar.

TABLE 7 RESERVOIR CHARACTERISTICS Depth of roof, m 300 Overall dimensions in the X, Y, Z directions, m 100, 720, 58.5 Thickness of the zone with oil and the water- 43.2, 15.3 bearing zone, m Permeability, horizontal, vertical, mD 10000, 3500  Porosity, fraction 0.37 Initial pressure @343.2 m, bar 32.2 Initial temperature, ° C. 17.0 Density of the oil, API 10 Viscosity of the oil, cP 3.8E+06 Initial water saturation, fraction volume of 0.22 pores Initial composition of the crude, mole fraction H₂S 0.00000 SAT 0.60752 ARO 0.14992 RES1 0.04071 RES2 0.14499 ASP1 0.01871 ASP2 0.03815

A first simulation was executed using stoichiometry (3). FIG. 4.1 presents the results of the simulation as a function of time of cumulative oil production, and the ratio of the steam/oil cumulative productions. The flow rate of oil produced in surface conditions and the bottom temperature of the injection well are shown in FIG. 4.2.

The simulated production of H₂S, expressed, as is customary in publications on this subject, in liters of H₂S per m³ of oil at the surface, is presented in FIG. 5, with the production of H₂S deduced from measurements between 2005 and 2012 on the Fisher Field published by the oil companies Encana and Cenovus, on the website of the Energy Resources Conservation Board (2012). The same figure shows the simulated production of H₂S obtained using stoichiometry (2) in the simulation, all other things remaining equal.

An X-Z map of the mole fraction of H₂S in the gas phase, after about 4 years of production, is shown in FIG. 6. This map is obtained from the results of the simulation with stoichiometry (2), but the qualitative return is about the same with stoichiometry (3): the highest concentrations of H₂S are observed at the limit of the steam chamber where there are simultaneously high temperatures and reagents in abundance. The behavior of the design section modeled, results at the wells and in the cells, is in overall agreement with expectations.

It can be seen in FIG. 5 that the production of H₂S obtained with stoichiometry (2), —which calibrated the experimental results of evolution of the SARA fractions as a function of time—, is much more in agreement with the field data than that obtained with stoichiometry (3), —which in addition calibrated the experimental production of H₂S—.

Moreover, a study was conducted of the sensitivity to various parameters of the simulations: size of the cells, effect of dissolution of H₂S in the aqueous phase, thermodynamics by correlation or by equation of state, variation of the conditions of pressure (initial pressure and injection pressure) in the range from 28 bar to 40 bar (for this range of pressures, the injection temperature varies in the range of 230-250° C.; in fact, as the steam injected is steam saturated with water, it will be recalled that the curve of water saturation pressure as a function of the temperature creates a relation that is biunivocal in injection pressure and injection temperature). In all cases, the results obtained, expressed in liters of H₂S per m³ of oil produced, are similar to those presented in FIG. 5, i.e. the results obtained with stoichiometry (2) are much more consistent with the field data than those obtained with stoichiometry (3).

In the simulations that were carried out (cf. FIG. 4.2), as well as in the reality of exploitation of the Fisher Field between 2005 and 2012, the period during which the field data was collected, the exploitation conditions aim to maintain the reservoir at temperature to conserve the reduction in oil viscosity connected with the temperature rise. As there is a close connection between temperature and pressure in the processes for injection of saturated steam, the reservoir is neither depressurized nor cooled, as is the case for the experimental reactor. If H₂S generated by the reactions of aquathermolysis is adsorbed on solids in the reservoir, there is no particular source of desorption without depressurization or cooling of the reservoir. As the hypothesis of such an adsorption phenomenon is plausible, there is a source of apparent disagreement between the experimental results of aquathermolysis and the measurements in the field, and the relative stoichiometry of sulfur between the solid and the H₂S can be used as a parameter for adjustment of this phenomenon, while preserving the other parameters of the thermokinetic model, parameters that are calibrated solely on the evolution of the SARA fractions.

Since the specific surface of the coke produced in situ by the reactions of aquathermolysis is not known, the values of the capacities for adsorption of H₂S obtained from the literature might not be relevant for the coke generated in situ by aquathermolysis. However, while the hypothesis according to which H₂S can be trapped by adsorption in the reservoir holds, the production of H₂S measured in the laboratory, modeled by stoichiometry (3), can be regarded as that which would correspond to maximum desorption, whereas the production of H₂S modeled by stoichiometry (2), which is of the order of magnitude of the field data, would take account of the H₂S trapped in the reservoir by adsorption on the coke. Taking into account the initial composition of the oil, assuming that the reactions have reached final equilibrium, and ascribing the difference between stoichiometry (2) and (3) to an effect of adsorption of H₂S on the COK, a capacity for adsorption can be calculated, which is thus estimated at about 0.09 gram H₂S per gram of the constituent COK for conditions of pressure and temperature at the places of reactions of about 33 bar and 240° C. This value is not inconsistent with the values of 2.9 grams of H₂S per gram of coke at 100 bar and 25° C. of Li et al. (2011), and of 0.02 g/g at atmospheric pressure and a temperature in the range of 200-250° C. of Itaya et al. (2011).

It can be seen that the methodology proposed for constructing a thermokinetic model usable in reservoir simulation based on the invention of Lamoureux-Var (2007) made it possible to obtain, once the thermokinetic model was introduced in a reservoir simulation at the field scale, a production of H₂S consistent with published data with much smaller adjustments of parameters than those employed in the methods of the prior art. 

1. Method of exploiting an underground deposit of hydrocarbons containing organosulfur compounds, characterized in that: i. an amount of hydrogen sulfide (H₂S) is determined, produced by a phenomenon of aquathermolysis induced by a thermal process such as injection of steam into said deposit, using the following steps: describing the hydrocarbons by means of a compositional representation using H₂S and four fractions: saturated compounds, aromatics, resins and asphaltenes; constructing a kinetic model on the basis of said compositional representation, starting from an elementary model obtained by mass balance for the element sulfur distributed within said fractions; constructing a thermodynamic model on the basis of said compositional representation; determining the amount of hydrogen sulfide (H₂S) produced, by performing a compositional reservoir simulation by means of a compositional and reactive thermal simulator, said simulator employing said kinetic model and said thermodynamic model; ii. the exploitation conditions of said deposit are determined as a function of said amount of hydrogen sulfide; iii. said hydrocarbons are produced by applying said exploitation conditions.
 2. Method according to claim 1, wherein the kinetic model is constructed assuming that the reactants of the H₂S generating reactions belong to the classes of resins and asphaltenes, and assuming that the products of said reactions belong to the set of H₂S, saturated compounds, aromatics and a pseudo-constituent of the solid type such as coke.
 3. Method according to claim 1, wherein said kinetic model comprises Nt constituents and Nr reactions, and a matrix Nr×Nt of stoichiometric coefficients of the various reactions is constructed; said stoichiometric coefficients being determined from an elementary reaction scheme obtained by mass balance for the element sulfur.
 4. Method according to claim 1, wherein said kinetic model is adjusted by simulating aquathermolysis experiments or by simulating the behavior of a field subjected to a thermal process, a field for which measurements of production allowing calculation of H₂S production are available.
 5. Method according to claim 4, wherein said kinetic model is adjusted by adjusting time constants for restoring a decrease in the resins and asphaltenes as a function of time, and/or by adjusting the relative stoichiometry between the saturated fractions and the aromatics, and/or by adjusting the relative stoichiometry between H₂S and a pseudo-constituent of the solid type such as coke.
 6. Method according to claim 1, wherein the compositional representation comprises: pseudo-constituents for representing fluid phases, and phases that can be made to become fluid, notably by the effect of temperature; at least one pseudo-constituent of the solid type (COK), such as coke; at least one constituent representing water.
 7. Method according to claim 1, wherein the fraction representing the saturated compounds represents, among the reaction products, the only fraction of the compounds not containing sulfur.
 8. Method according to claim 1, wherein said amount of hydrogen sulfide is compared against an amount measured in the past, and parameters of said kinetic model and/or of said thermal model are adjusted.
 9. Method according to claim 8, wherein production of H₂S by said deposit is predicted from said adjusted models.
 10. Method according to claim 1, wherein the exploitation conditions are determined by adapting completion materials and/or gas treatment devices.
 11. Method according to claim 1, wherein the exploitation conditions are modified by adapting the conditions of steam injection.
 12. Method according to claim 1, wherein said amount of hydrogen sulfide is compared against a maximum legal content, and the exploitation conditions are determined so as to keep hydrogen sulfide production below said maximum legal content. 